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Five embeddings of one simple group


Authors: Ivan Cheltsov and Constantin Shramov
Journal: Trans. Amer. Math. Soc. 366 (2014), 1289-1331
MSC (2010): Primary 14J30, 14J70, 13F15, 14B05
DOI: https://doi.org/10.1090/S0002-9947-2013-05768-6
Published electronically: June 11, 2013
MathSciNet review: 3145732
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Abstract: We propose a new method to study birational maps between Fano varieties based on multiplier ideal sheaves. Using this method, we prove equivariant birational rigidity of four Fano threefolds acted on by the group  $ \mathrm {A}_6$. As an application, we obtain that $ \mathrm {Bir}(\mathbb{P}^{3})$ has at least five non-conjugate subgroups isomorphic to  $ \mathrm {A}_{6}$.


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Additional Information

Ivan Cheltsov
Affiliation: Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
Email: I.Cheltsov@ed.ac.uk

Constantin Shramov
Affiliation: Steklov Mathematical Institute, Gubkina Str. 8, 119991, Moscow, Russia
Email: shramov@mccme.ru

DOI: https://doi.org/10.1090/S0002-9947-2013-05768-6
Received by editor(s): February 1, 2011
Received by editor(s) in revised form: November 27, 2011
Published electronically: June 11, 2013
Additional Notes: The first author was supported by the grants NSF DMS-0701465 and EPSRC EP/E048412/1
The second author was supported by the grants RFFI 08-01-00395-a, NSh-1987.2008.1 and EPSRC EP/E048412/1.
Article copyright: © Copyright 2013 American Mathematical Society